Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace

Three coins are tossed once. Let $A$ denote the event ' three heads show ', $B$ denote the event ' two heads and one tail show ' , $C$ denote the event ' three tails show and $D$ denote the event 'a head shows on the first coin '. Which events are Compound ?

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam, $60\%$ candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is.

Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is $6$

If $A$ and $B$ are two independent events such that $P\,(A \cap B') = \frac{3}{{25}}$ and $P\,(A' \cap B) = \frac{8}{{25}},$ then $P(A) = $